The Laplace limit
An earlier post discussed how to solve Kepler’s equation M =В E в€’В e sin(E) using a sine series. You could also solve Kepler’s equation using a power series, which Lagrange did i...
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An earlier post discussed how to solve Kepler’s equation M =В E в€’В e sin(E) using a sine series. You could also solve Kepler’s equation using a power series, which Lagrange did i...
Kepler solved his eponymous equation M =В E в€’В e sin(E) by finding a fixed point of E = M + e sin(E). So guess a value ofВ E and stick it into the right hand side. Then plug that...
I ran across the approximation e ≈ 2721/1001 recently. What makes this remarkable is its accuracy relative to the size of the denominator. You can create a trivial approxima...
Yesterday I wrote a post showing that the trapezoid rule evaluates the integral very efficiently. But how do we know what the exact integral is for comparison? If you ask Mathemati...
Let f be an even function with period ПЂ. Then the following remarkable theorem by Lobachevsky holds. This theorem is useful in Fourier analysis and signal processing. It’s useful...
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